Myhill-Nerode Relations on Automatic Systems and the Completeness of Kleene Algebra

It is well known that finite square matrices over a Kleene algebra again form a Kleene algebra. This is also true for infinite matrices under suitable restrictions. One can use this fact to solve certain infinite systems of inequalities over a Kleene algebra. Automatic systems are a special class of infinite systems that can be viewed as infinite-state automata. Automatic systems can be collapsed using Myhill–Nerode relations in much the same way that finite automata can. The Brzozowski derivative on an algebra of polynomials over a Kleene algebra gives rise to a triangular automatic system that can be solved using these methods. This provides an alternative method for proving the completeness of Kleene algebra.

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: Dexter Kozen
• Keywords: Automatic Systems, Infinite Systems, Kleene Algebra, STACS 2001, Theoretical Computer Science